ABSTRACT
Sum of two convex functions is a convex function. However, the sum of two quasi-convex functions is not necessarily a quasi-convex function. Quasi-convexity is a generalization of convexity. The set of all quasi-convex functions contains the set of all convex functions. A general method to solve quasi-convex optimization problem uses the representation of the sublevel sets of a quasi-convex function via a family of convex inequalities. A simple algorithm for solving quasi-convex optimization problem by using bisection that solves the convex feasibility problem at each step. In microeconomics, quasi-concave utility functions imply that consumers have convex preferences. Quasi-convex functions are important in game theory, industrial organization, and general equilibrium theory, particularly for applications of Sion's minmax theorem, which is a generalization of von Neumann's minmax theorem.
